Question

I need help figuring this out of the geometric mean of this word problem. I'll draw the figure out so be patient. Medal will be rewarded for your patronage! :D

Answer 1

<i+<2+(<5+<6)=180 or <1+<2+90=180,<1+<2=180-90=90 ...(1)
<1+<5+90=180, <1+<5=90 .....(2)
<2+<6+90=180, <2+<6=90 ......(3)
from (1) and (2),
<1+<2=<1+<5
or <2=<5
from (1) and (3)
<1+<2=<2+<6
<1=<6
triangles (2) and (3) are similar.
Hence sides are proportional.
\[\frac{ BD }{ DC }=\frac{ AD }{ BD },(BD)^{2}=AD*DC=x*9=9x,BD=3\sqrt{x}\]